5(2x-3)+3x=-10+7/3x

Solution for 5(2x-3)+3x=-10+7/3x equation:

5(2x-3)+3x=-10+7/3x

We move all terms to the left:

5(2x-3)+3x-(-10+7/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5(2x-3)+3x-(7/3x-10)=0

We add all the numbers together, and all the variables

3x+5(2x-3)-(7/3x-10)=0

We multiply parentheses

3x+10x-(7/3x-10)-15=0

We get rid of parentheses

3x+10x-7/3x+10-15=0

We multiply all the terms by the denominator


3x*3x+10x*3x+10*3x-15*3x-7=0

Wy multiply elements

9x^2+30x^2+30x-45x-7=0

We add all the numbers together, and all the variables

39x^2-15x-7=0

a = 39; b = -15; c = -7;
Δ = b2-4ac
Δ = -152-4·39·(-7)
Δ = 1317
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{1317}}{2*39}=\frac{15-\sqrt{1317}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1317}}{2*39}=\frac{15+\sqrt{1317}}{78}
$